Probing the four-fermion operators via the transverse double spin asymmetry at the Electron-Ion Collider

The chirality-flipping operators of light fermions are currently poorly constrained by experimental analyses due to the lack of interference with Standard Model (SM) amplitudes in traditional observables. In this work, we propose to investigate the semi-leptonic scalar/tensor four-fermion operators of electron and quarks through the transverse double spin asymmetry (DSA) at Electron-Ion Collider, where both the electron and proton beams could be highly transversely polarized. Due to the chirality-flipping nature of these operators, we demonstrate that their interference with the SM results in an unsuppressed contribution to the DSA, and could lead to non-trivial azimuthal $\cos2\phi$ and $\sin2\phi$ distributions that are linearly dependent on their Wilson coefficients. This new method has the potential to significantly improve the current constraints on these scalar/tensor four-fermion operators without relying on theoretical assumptions about other types of new physics effects, particularly for the tensor type operator of the $u$-quark. Additionally, our findings indicate that both the real and imaginary parts of these operators can be simultaneously constrained and offer a new opportunity for probing potential $CP$-violation effects. However, it is important to note that these results would be sensitive to the quark transversity distributions, which are currently poorly constrained by the experimental data, but could be significantly improved at the upcoming Electron-Ion Collider. Therefore, our work opens up a new avenue to utilize this new spin asymmetry for exploring the new physics effects from the scalar/tensor four-fermion operators.